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Question

The area of an isosceles triangle ABC is 48 cm2, where AB = AC. If the perimeter of the triangle and its altitude AD on BC are 32 cm and 8 cm respectively, then the length of the equal sides is equal to

A
8 cm
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B
10 cm
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C
12 cm
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D
13 cm
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Solution

The correct option is B 10 cm

Area of ΔABC=12×Base×Altitude
48=12×BC×AD
48×2=BC×8 (AD=8cm)
BC=12cm …..(i)
Perimeter of ΔABC=32cm
AB+BC+AC=32
2AB+12=32 (AB=AC and BC=12cm)
AB=32122=10cm
Thus, the length of the equal sides of ΔABC is 10 cm.
Hence, the correct answer is option (b).

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